Geometric Algebra in 3D - The Vector-Bivector Product (Part 2)
In this second part, we'll investigate the algebraic properties and geometric meaning of this extended dot and wedge product. We'll see that vectors in the plane of a bivector anticommute with the bivector under the geometric product and vectors orthogonal to the plane of a bivector will
From playlist Math
Geometric Algebra in 3D - The Vector-Bivector Product (Part 1)
After having set up G(3), let's now investigate a particular geometric product, namely, the product between vector and bivector. We'll see that such a product in general splits into a vector part and the trivector part. Similar to the geometric product between vectors, we'll call the lower
From playlist Math
Geometric Algebra - Duality and the Cross Product
In this video, we will introduce the concept of duality, involving a multiplication by the pseudoscalar. We will observe the geometric meaning of duality and also see that the cross product and wedge product are dual to one another, which means that the cross product is already contained w
From playlist Geometric Algebra
Dominique MANCHON - On Multiple Zeta Values and their q-analogues
Multiple zeta values are real numbers which appeared in depth one and two in the work of L. Euler in the Eighteenth century. They first appear as a whole in the work of J. Ecalle in 1981, as infinite nested sums. A systematic study starts one decade later with M. Hoffman, D. Zagier and M.
From playlist Algebraic Structures in Perturbative Quantum Field Theory: a conference in honour of Dirk Kreimer's 60th birthday
Dot products, Pythagoras' theorem, and generalizations | Wild Linear Algebra A | NJ Wildberger
Here we begin to study metrical geometry from the framework of linear algbra, but we do so in a novel, completely algebraic way. The starting point is the dot product, motivated by Pythagoras' theorem but logically independent of any prior understanding of Euclidean geometry. The main pro
From playlist WildLinAlg: A geometric course in Linear Algebra
Ex 2: Properties of Cross Products - Cross Product of a Sum and Difference
This video explains how to find the cross product of a sum and difference of two vectors. Site: http://mathispower4u.com
From playlist Vectors in Space (3D)
Some new results on rationality (Lecture - 01) by Claire Voisin
Infosys-ICTS Ramanujan Lectures Some new results on rationality Speaker: Claire Voisin (College de France) Date: 01 October 2018, 16:00 Venue: Madhava Lecture Hall, ICTS campus Resources Lecture 1: Some new results on rationality Date & Time: Monday, 1 October 2018, 04:00 PM Abstra
From playlist Infosys-ICTS Ramanujan Lectures
Abstract Algebra | Properties of isomorphisms.
We prove some important properties of isomorphisms. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
The vector cross-product is another form of vector multiplication and results in another vector. In this tutorial I show you a simple way of calculating the cross product of two vectors.
From playlist Introducing linear algebra
In this tutorial I cross the bridge between a standard algebraic function and products sets, as well as mappings. I show the three types of mappings, namely injective (one-to-one), surjective (onto), and their combination, a bijection.
From playlist Abstract algebra
Lie groups: Baker Campbell Hausdorff formula
This lecture is part of an online graduate course on Lie groups. We state the Baker Campbell Hausdorff formula for exp(A)exp(B). As applications we show that a Lie group is determined up to local isomorphism by its Lie algebra, and homomorphisms from a simply connected Lie group are deter
From playlist Lie groups
Isomorphisms in abstract algebra
In this video I take a look at an example of a homomorphism that is both onto and one-to-one, i.e both surjective and injection, which makes it a bijection. Such a homomorphism is termed an isomorphism. Through the example, I review the construction of Cayley's tables for integers mod 4
From playlist Abstract algebra
Ralph Kaufmann: Graph Hopf algebras and their framework
The lecture was held within the framework of the Hausdorff Trimester Program: Periods in Number Theory, Algebraic Geometry and Physics. Abstract: I will discuss recent results linking the Hopf algebras of Goncharov for multiple zetas, the Hopf algebra of Connes and Kreimer for renormalis
From playlist Workshop: "Amplitudes and Periods"
Yinhuo Zhang: Braided autoequivalences, quantum commutative Galois objects and the Brauer groups
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Algebra
Claudia Pinzari: "Weak quasi-Hopf algebras associated to Verlinde fusion categories"
Actions of Tensor Categories on C*-algebras 2021 "Weak quasi-Hopf algebras associated to Verlinde fusion categories" Claudia Pinzari - Sapienza Università di Roma Abstract: Unitary modular fusion categories arise in various frameworks. After a general overview on unitarity, we discuss th
From playlist Actions of Tensor Categories on C*-algebras 2021
Guangyu Zhu: The Galois group of the category of mixed Hodge Tate structures
The lecture was held within the framework of the Hausdorff Trimester Program: Periods in Number Theory, Algebraic Geometry and Physics. Abstract: The category of mixed Hodge-Tate structures over Q is a mixed Tate category of homological dimension one. By Tannakian formalism, it is equiva
From playlist Workshop: "Periods and Regulators"
On the classification of fusion categories – Sonia Natale – ICM2018
Algebra Invited Lecture 2.5 On the classification of fusion categories Sonia Natale Abstract: We report, from an algebraic point of view, on some methods and results on the classification problem of fusion categories over an algebraically closed field of characteristic zero. © Interna
From playlist Algebra
Matt SZCZESNY - Toric Hall Algebras and infinite-dimentional Lie algebras
The process of counting extensions in categories yields an associative (and sometimes Hopf) algebra called a Hall algebra. Applied to the category of Feynman graphs, this process recovers the Connes-Kreimer Hopf algebra. Other examples abound, yielding various combinatorial Hopf algebras.
From playlist Algebraic Structures in Perturbative Quantum Field Theory: a conference in honour of Dirk Kreimer's 60th birthday
Introduction to quantized enveloping algebras - Leonardo Maltoni
Quantum Groups Seminar Topic: Introduction to quantized enveloping algebras Speaker: Leonardo Maltoni Affiliation: Sorbonne University Date: January 21, 2021 For more video please visit http://video.ias.edu
From playlist Quantum Groups Seminar
Multivariable Calculus | The Cross Product
We define the cross product, give a few examples, and state a few properties. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Vectors for Multivariable Calculus